Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Knot/Knotting Practice in Craft and Space

Knot/knotting Practice in Craft and Space is a three part research-creation project that used a study of knotting techniques to locate craft in an expanded field of spatial practice. The first part consisted of practical, studio based exercises in which I worked with various natural and synthetic fibres to learn common knotting techniques. The second part was an art historical study that combined craft and architecture history with critical theory related to the social production of space. The third part was an exhibition of drawing and knotted objects titled Opening Closures. This document unifies the lines inquiry that define my project. The first chapter presents the art historical justification for knotting to be understood as a spatial practice. Nineteenth-century German architect and theorist Gottfried Semper’s idea that architectural form is derived from four basic material practices allies craft and architecture in my project and is the point of departure from which I make my argument. In the second chapter, to consider the methodological concerns of research-creation as a form of knowledge production and dissemination, I adopt the format of an instruction manual to conduct an analysis of knot types and to provide instructions for the production of several common knots. In the third chapter, I address the formal and conceptual underpinnings of each artwork presented in my exhibition. I conclude with a proposal for an expanded field of spatial practice by adapting art critic and theorist Rosalind Krauss’s well-known framework for assessing sculpture in 1960s.